Rees Kato–Nakayama Abstract Corridor Packet and the Literal Cell-Assignment Gate
Correction
Date: 2026-08-16
The checker proves the positive Kato–Nakayama five-cell packet of each
multiplicity-sensitive product-branch Rees exceptional interval. It does not
enumerate K6 faces or entry143 [S,H] generators. The earlier wording that
called its declared five-cell basis a literal entry143 spatial pushforward
was too strong and is retracted here.
For the labelled Rees equation [ cA-abB=0, ] the positive exceptional (mathbf P^1) is an oriented interval with fixed sections ([1:0]), ([0:1]), and intrinsic marked overlap ([1:1]). Preservation of the labelled equation forces any diagonal projective rescaling to be common, so it is projectively trivial.
The abstract packet has vertices (o,m,i), edges (e_L,e_R), and [ d e_L=m-o,\qquad d e_R=i-m. ] Tensoring with the complete two-normal Boolean packet and both conductor Tor grades gives 240 abstract labelled rows. The coefficient matrix is the identity, has rank 240, and has 240 unit Smith factors. Ninety-six occurrence-line factors cancel by principal-dual evaluation; no base section or integer is inverted. The total cellular–Boolean differential squares to zero, and rotation/reflection preserve the packet.
Exact remaining gate
No function in the checker maps (o,m,i,e_L,e_R) to actual K6 faces or to entry143 generators. Consequently it proves neither literal endpoint/facet restrictions nor a spatial corestriction square.
The first missing datum is a support-typed assignment from each Rees/KN packet to an actual marked K6 corridor, expanded on every occurrence, normal-circle, Tor, and Čech state. It must then be compared on overlaps and attached to the generic (Q) top. Entries 258–260 show that an ordinary face-poset assignment cannot provide the cross-sheet and maximal-cone cells; the eventual map must be extraordinary/mixed-variance.
Until that assignment exists, the global normalization kernel, pointed endpoint/Q mapping fiber, (p_{partial,Q}), its Bockstein, and the (D_8)/Jordan tests remain undefined.
Executable evidence
Checker:
research/voevodsky/check_dp6_rees_kn_literal_corridor_pushforward.rs
The current checker output explicitly records that K6 faces and entry143 generators are not enumerated and that the literal cell assignment is unconstructed.
Outcome contract
{
"claim": "The labelled product-branch Rees exceptional P1 has a canonical positive KN five-cell subdivision with a saturated abstract corridor packet, compatibly with Boolean normals, both Tor grades, reflection, and D3.",
"status": "proved_scoped_positive_KN_Rees_abstract_corridor_packet",
"scope": "six local labelled Rees/KN abstract five-cell packets; literal K6/entry143 cell assignment, global normalization-conductor descent, and Q attachment excluded",
"matrix": {
"ordered_cones": 6,
"corridor_cells_per_cone": 5,
"boolean_states": 4,
"tor_grades": [0, 1],
"abstract_labelled_rows": 240,
"occurrence_principal_dual_evaluations": 96,
"rank": 240,
"smith_unit_factors": 240,
"torsion": false
},
"geometry": {
"intrinsic_marked_overlap": "[1:1]",
"independent_Rees_rescaling_allowed": false,
"proper_positive_KN_packet": true,
"D3": true,
"reflection": true
},
"K6_faces_enumerated": false,
"entry143_generators_enumerated": false,
"literal_entry143_cell_assignment_constructed": false,
"unconstructed": [
"literal K6 face and entry143 [S,H] cell assignment",
"global normalization-conductor six-functor descent",
"global W012/qSigma attachment inside the same kernel",
"pointed endpoint/Q mapping fiber",
"p_partial_Q and Bockstein",
"D8 and Jordan coherence"
],
"checker": "research/voevodsky/check_dp6_rees_kn_literal_corridor_pushforward.rs",
"graph_admission_claimed": false
}